A128851 Denominators of the continued fraction convergents of the decimal concatenation of the prime-indexed primes.

1, 2, 3, 17, 20, 37, 94, 131, 225, 581, 806, 1387, 2193, 3580, 63053, 66633, 129686, 196319, 522324, 718643, 2678253, 8753402, 20185057, 69308573, 436036495, 941381563, 9849852125, 10791233688, 20641085813, 31432319501, 83505724815

Offset

0,2

Comments

Prime-indexed primes (pips) or primeth primes 3, 5, 11, 17, 31, 41, 59, 67, ... are concatenated and then preceded by a decimal point to create the fraction N = .35111731415967... This number is then evaluated with n=0, m=steps to iterate, x = N, a(0)=floor(N) using the loop: do a(n)=floor(x) x=1/(x-a(n)) n=n+1 loop until n=m.

Links

Table of n, a(n) for n=0..30.

Prog

(PARI) cattpips(n) = { a="."; forprime(x=2, n, a=concat(a, prime(x))); a=eval(a) }
cfrac2(m, f) = { default(realprecision, 1000); cf = vector(m+10); cf = contfrac(f); for(m1=1, m-1, r=cf[m1+1]; forstep(n=m1, 1, -1, r = 1/r; r+=cf[n]; ); numer=numerator(r); denom=denominator(r); print1(denom", "); ) }

Crossrefs

Cf. A128850 (numerators).

Sequence in context: A121409 A041295 A128845 * A078737 A041981 A197223

Adjacent sequences: A128848 A128849 A128850 * A128852 A128853 A128854

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 16 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved